Rapid reconnaissance of a model of a chemical oscillator by numerical continuation of a bifurcation feature of codimension 2

Many models have been proposed for the well-known Belousov-Zhabotinskii reaction. Partly for this reason, but also because the dimension of the models' parameter spaces are very high, the phenomenology of even the most popular models has been investigated only lightly. The existence in the models of free parameters, i.e., those for which no values are supplied a priori, spreads the investigation even thinner. Consequently, the accuracy with which the models are capable of reproducing experimental phenomena is something that remains unknown. It therefore appears that there might be a use, in the investigation of such models, for a method by which large regions of a parameter space could be reconnoitered in some way. We describe a numerical calculation that constitutes a reconnaissance of a four-dimensional parameter subspace of a seven-species model of the Belousov-Zhabotinskii reaction. The calculation consists of following, or "continuing," a bifurcation feature of codimension 2 throughout the parameter subspace. By comparing the results with experiment, we are able to circumscribe the region of the free-parameter space where qualitative agreement is possible, and we determine that, with the rate constants originally given by the authors of the model, quantitative agreement with experiment does not exist in any region of the free-parameter space. Moreover, we are able to determine that if a revised set of rate constants from the literature is used, nowhere in the free-parameter space is the model even qualitatively correct. We believe the method described may be helpful beyond the context discussed here.